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People with college degrees make $1 million more over their careers than people without, and they are less likely to be unemployed. So if we open college doors to everyone, the country will be better off.

So goes the defense for the grand expansion—in price and in volume—of the higher education business over the past few decades. Is it possible that the premise is just wrong? In that case the producers of education have perpetrated a fraud on the rest of us.

It’s a clever fraud, built around a subtle logical flaw called the fallacy of composition. That is the fallacy that has you thinking a phenomenon true for any one person or thing can be simultaneously true for every person or thing. The classic illustration of the fallacy goes like this: One person can see better at the ballgame by standing up, so if everybody in the stadium stands up they will all see better.

If one person can better his lot in life by getting a B.A., it does not follow that the economy will be stronger when everyone has a B.A. To see what’s going on, imagine that the country’s 140 million jobs are ranked by the extent to which they demand verbal and numerical skills. At the top, math professor; at the bottom, janitor.

Average pay in the top half is higher than average pay in the bottom half. There is, of course, great variation within each group: The more academic one has adjunct professorships paying $15,000 and the less academic one has baseball jobs at $15 million. But averages are what matter here.

Now consider another feature of American life, that employers usually don’t give ability tests to their applicants. Either they have lawyers telling them they can’t or they are just squeamish. If they want to select for intellectual skills they must resort to a proxy measure. A degree serves that purpose. If half the people in the work force have a bachelor’s degree and half don’t, the half with the degree are going to wind up with most of the jobs in the upper half of our list.

College graduation is an imperfect measure of ability. Some brilliant entrepreneurs struggle with school because of dyslexia. Some clunkers from well-connected families wind up with Ivy League credentials and get to be president of something. But, absent a better sorting mechanism, the degree will influence who gets ahead.

This credentialing business can go on even in the absence of any subject matter connection between the school course and the job. A first in classics at Oxford or Cambridge used to be the entry ticket to a plum job in the British foreign service, not because fluency in Latin would come in handy, but because it was an indicator of intelligence.

In a country where half the population went to college, would it pay for one person to borrow money and struggle to get a degree? Maybe. It might get him out of the car wash and into an accounts receivable job. It does not follow, however, that if everyone goes to college then everyone will wind up with a top-half job.

Politicians declare that in a land of opportunity, everyone should go to college. The egalitarianism behind this notion is hard to fault. After all, there is going to be some unfairness in a system that has only half the population getting a four-year degree. There will be rich kids who land legacy slots at fancy colleges, poor kids who fall behind while attending rotten elementary schools.

But an everyone-goes system is hugely wasteful. Richard Vedder, an Ohio University economist who helps run the Center for College Affordability & Productivity, cites this interesting statistic: 115,000 janitor jobs in the U.S. are held by people with bachelor’s degrees. He says economic output would be higher if the federal government didn’t take quite so many 18- to 22-year-olds out of the workforce and send them off to college on Pell grants.

Charles Murray, a scholar at the American Enterprise Institute, thinks that the four-year bachelor's degree has turned into something of a farce. Many of the students attending college shouldn't be there, he has written. Many of the courses do nothing to make the student more valuable to an employer. Why not junk the B.A. and replace it with a system of certification (in programming skills, for example)? The Educational Testing Service (the SAT outfit) could make a nice business of this.

Murray is controversial because he takes the intellectual stratification of our society as a given. This sort of thinking conflicts with politicians’ egalitarian pronouncements. But egalitarianism that doesn’t deliver job skills doesn’t make lives better.

If thinkers like Vedder and Murray had more sway, some of the kids struggling with algebra in high school would be studying welding or car mechanics instead, and many of the ones whiling away four years on liberal arts courses would be studying nursing or software instead.

For company in misery, unemployed liberal arts grads can take note that in this unforgiving economy a sheepskin from even an elite school doesn’t guarantee career success. Someone recently forwarded to me an ad that was posted on the electronic bulletin board for parents at a prestigious private school in Manhattan. Here it is, with names and some other details omitted:

My sister recommended a close friend and former classmate at Harvard who is looking for babysitting jobs in the NYC area. He studied psychology and graduated in 2011, and is currently working part-time as an intern in Midtown. He is a caring, gentle guy and is absolutely great with children.

If he didn’t get a scholarship the poor fellow must have spent $190,000 on that Harvard degree.